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In the ordinary relational model, relations are sets of tuples, which by definition do not contain “duplicate” entries. However, RDBMSs typically implement a variation of this model where relations are bags (or multisets) of tuples, with duplicates allowed. Formally, a bag is a mapping of tuples to natural number multiplicities; a set can be viewed as a special case of a bag where all tuple multiplicities are 0 or 1. The operations of the relational algebra are extended to operate on bags by defining their action on tuple multiplicities. RDBMSs based on bags rather than sets are said to implement bag semantics (rather than set semantics). Duplicates may occur at multiple levels: in source relations, in materialized views, or in query answers. A variation of bag semantics called bag-set semanticsis obtained by requiring source relations to be sets, while allowing views and query answers to contain duplicates. Bag-set...
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Recommended Reading
Abiteboul S., Hull R., and Vianu V. Foundations of Databases. Addison-Wesley, Reading, MA, 1995.
Buneman P., Naqvi S., Tannen V., and Wong L. Principles of programming with complex objects and collection types. Theor. Comput. Sci., 149(1):3–48, 1995.
Chaudhuri S. and Vardi M.Y. Optimization of real conjunctive queries. In Proc. 12th ACM SIGACT-SIGMOD-SIGART Symp. on Principles of Database Systems, 1993.
Cohen S. Equivalence of queries combining set and bag-set semantics. In Proc. 25th ACM SIGACT-SIGMOD-SIGART Symp. on Principles of Database Systems, 2006, pp. 70–79.
Cohen S., Nutt W., and Serebrenik A. Rewriting aggregate queries using views. In Proc. 18th ACM SIGACT-SIGMOD-SIGART Symp. on Principles of Database Systems, 1999.
Dayal U., Goodman N., and Katz R.H. An extended relational algebra with control over duplicate elimination. In Proc. 1st ACM SIGACT-SIGMOD Symp. on Principles of Database Systems, 1982, pp. 117–123.
Green T.J. Containment of conjunctive queries on annotated relations. In Proc. 12th Int. Conf. on Database Theory, 2009.
Grumbach S., Libkin L., Milo T., and Wong L. Query languages for bags: Expressive power and complexity. SIGACT News, 1996, p. 27.
Ioannidis Y.E. and Ramakrishnan R. Containment of Conjunctive Queries: Beyond Relations as Sets. ACM TODS, 20(3):288–324, 1995.
Jayram T.S., Kolaitis P.G., and Vee E. The containment problem for real conjunctive queries with inequalities. In Proc. 25th ACM SIGACT-SIGMOD-SIGART Symp. on Principles of Database Systems, 2006.
Klausner A. and Goodman N. Multirelations – semantics and languages. In VLDB, 1985.
Klug A.C. Equivalence of relational algebra and relational calculus query languages having aggregate functions. J. ACM, 29(3):699–717, 1982.
Lovász L. Operations with structures. Acta Math. Hungarica, 18(3–4):321–328, 1967.
Mumick I.S., Pirahesh H., and Ramakrishnan R. The magic of duplicates and aggregates. In Proc. 16th Int. Conf. on Very Large Data Bases, 1990, pp. 264–277.
Mumick I.S. and Shmueli O. Finiteness properties of database queries. In Proc. 4th Australian Database Conf. Brisbane, Australia, February 1993.
Nutt W., Sagiv Y., and Shurin S. Deciding equivalences among aggregate queries. In Proc. 17th ACM SIGACT-SIGMOD-SIGART Symp. on Principles of Database Systems, 1998, pp. 214–223.
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Green, T.J. (2009). Bag Semantics. In: LIU, L., ÖZSU, M.T. (eds) Encyclopedia of Database Systems. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-39940-9_979
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